Hydrofoil Of Finite Span Research Articles

Dynamics of dispersed bubbly flow over a lifting surface: Gas diffusion and bubble breakup effects

The modification of the bubble nuclei population by the presence of a finite-span hydrofoil is modeled numerically using an Eulerian-Lagrangian approach. The unsteady liquid flow field is simulated using Navier-Stokes equations, while the bubbles, initiating from nuclei in the free stream and emitted from boundaries, are tracked using a Lagrangian approach. The effects of including gas diffusion, wall nucleation, and bubble breakup on nuclei distribution downstream of hydrofoil are studied. The inclusion of gas diffusion is found to significantly increase the size of the bubbles downstream. Also, inclusion of boundary nucleation is found to significantly increase the total number of large bubbles collected in the wake as compared to accounting for free nuclei alone. Bubble breakup, modeled using instability analysis and experimental observations, is seen to result in a significant increase in the number of small and mid-size bubbles, at the expense of the large size bubbles.

Experimental validation of lift and drag forces on an asymmetrical hydrofoil for seafloor anchoring applications

Tidal power can be described as harnessing the kinetic energy of the in and out flows known as tides created by the changing gravitational pull of the moon and the sun on the oceans of the world. As the relative positions of the sun and moon can be accurately predicted, so can the resultant tidal movements, making tidal energy such a valuable resource and an attractive option for renewable power generation. However, the high costs and difficulties associated with the deployment of underwater turbines, which includes anchoring, are prohibitive factors in the widespread utilisation of tidal power technology. Existing turbine fixation methods are primarily based on the use of large gravity anchors or monopole structures to secure the turbine to the seabed. In an effort to reduce size, environmental impact on the seafloor and installation cost, a hydrofoil-based anchor could be considered. The objective of this study is to experimentally test the lift and drag force behaviour of a finite-span hydrofoil with endplates, whose profile was selected based on simplified two-dimensional (2D) numerical simulations using the vortex panel method. A customised lift and drag force measurement system for this prototype hydrofoil was designed, fabricated and calibrated, and subsequently installed and tested in the Dutch Tidal Testing Centre (TTC) in Den Oever, the Netherlands. A series of tests with force and flow velocity measurements are described for different angles-of-attack under realistic tidal flow conditions. Results for the lift and drag coefficients as a function of angle-of-attack are compared to numerical simulation data and revealed that the real-world lift force is predicted well, whereas the drag force is underpredicted by the numerical predictions. These findings provide useful information for the design of anchoring systems based of hydrofoil profiles.

몰수 심도가 작은 고속 수중익 주위의 속도장 측정

A set of experiments was carried out for obtaining the velocity field around the hydrofoil of finite span, using a wing of the NACA 0012 section in a circulating water channel. DPIV technique was used to measure the velocity field, and the velocity measurements along the span were done for 3 speeds, 3 submerged depths, and 4 angles of attack. Experimental data are compared with the theoretical assumptions, as well as the numerical findings by Lee and Lee(2004). Special care is given to the flow near the tips and in the region close to the leading edge. Though indirect, using the measured data of the velocity, it is now possible to compare the aerodynamic and the hydrodynamic strength of the circulation distribution of a wing in the framework of the lifting-line theory.

몰수심도가 작은 고속 수중익 주위의 유동장에 대한 수치계산

In order to better understand the characteristics of the flow field around the submerged hydrofoil of finite span with high speed and shallow submergence. a numerical code which can solve the flow around a fast lifting body under the free surface was developed and used to obtain various interesting features of the flow. The code was based on the panel method of Hess( 1972), and the free surface condition was linearized to conform with the assumption of the high Froude number. It is shown that the effect of the change of submerged depth. angle of attack and aspect ratio upon the sectional lift coefficient is rather significant for the case of the chosen example wing, which has the rectangular planform. Since Lee(2002)'s theoretical results were for the wing of elliptical planform, the direct comparison of the two results was not possible. It seems that more computational results are in need to compare the theoretical and the numerical prediction in detail.

Direct Numerical Simulation of Unsteady Finite-Span Hydrofoil Flow

The tip-vortex flow over a finite-span hydrofoil with laminar separation on the hydrofoil surface was numerically studied by computing the three-dimensional unsteady Navier-Stokes equations. The computations were direct numerical simulations of all resolvable structures without adding a turbulence model. The topological structure of unsteady separated flow and the influence of the unsteady laminar separated flow on the tip vortex for both swept and unswept hydrofoils were qualitatively investigated. The secondary flow induced by the swept planform played an important role in the unsteadiness of the tip vortex. The interaction between the tip vortex and the unsteady laminar separated flow became stronger as the sweep angle was increased

Numerical Study of the Steady-State Tip Vortex Flow Over a Finite-Span Hydrofoil

The flow over a finite-span hydrofoil creating a tip vortex was numerically studied by computing the full Navier-Stokes equations. A good agreement in pressure distribution and oil flow pattern was achieved between the numerical solution and available experimental data. The steady-state roll-up process of the tip vortex was described in detail from the numerical results. The effect of the angle of attack, the Reynolds number, and the hydrofoil planform on the tip vortex was investigated. The axial and tangential velocities within the tip-vortex core in the near-field wake region were greatly influenced by the angle of attack. A jet-like profile in the axial velocity was found within the tip-vortex core at high angle of attack, while a wake-like profile in the axial velocity was found at low angle of attack. Increasing the Reynolds number was found to increase the maximum axial velocity, but only had a slight impact on the tangential velocity. Finally, a swept hydrofoil planform was found to attenuate the strength of the tip vortex due to the low-momentum boundary layer traveling into the tip vortex on the suction side.

VORTEX LATTICE METHOD FOR A STRAIGHT HYDROFOIL NEAR A FREE SURFACE

The paper presents a vortex lattice method for the calculation of lift on a straight hydrofoil of finite span near the free surface of an infinitely deep fluid. The velocity field induced by the vortex lattice satisfies the linearized free surface boundary condition and the radiation condition. Lift calculations are compared with experimental results for a 5.11 aspect ratio hydrofoil of the circular arc type. Two options regarding the path of the trailing vortices are examined, i.e. that the trailing vortices leave the hydrofoil directly from the camber surface or via the trailing edge. It is shown that for moderate effective angles of attack the results are very similar, and that the first option, which is simpler and computationally more efficient than the second, is sufficiently accurate for practical purposes. The method was also used to compute the variation of hydrodynamic characteristics with depth of submergence and Froude number for a flat plate of finite span. Results are presented for aspect ratios of 2, 5 and 10 respectively.

An experiment of cavitating flow around a finite span hydrofoil

This paper describes the experimental results of a finite span hydrofoil of NACA0012 section with elliptic planform (aspect ratio of 3).Lift and drag coefficients were measured at two angles of attack (α=10 and 20 deg.), where the cavitation number was changed from non-cavitating condition to super-cavitating condition.The pressure distribution of the hydrofoil and the wake distribution were measured at some typical cases. With this experiment the following results are obtained : (1) As the cavity grows, the ratio of cavity length to chord length becomes larger near the tip.(2) Under the non-cavitating condition or the condition of tip vortex cavitation there is a velocity acceleration near the tip-vortex. This acceleration changes to deceleration after inception of sheet type cavitation.

Finite Difference Calculation of Cavitating Flow around a Finite Span Hydrofoil

Characteristics of cavitating flow around a finite span hydrofoil are studied by a finite difference computation using Bubble Two-phase Flow model. The flow with Reynolds number of 103 is calculated at the angle of attack of 10 deg. on a NACA 0012 hydrofoil with elliptic planform of aspect ratio of 3.The mechanisms of the cavitating flow, particularly the relationships between the vortex system around the hydrofoil and the cavitation, are investigated with the use of the high spatial resolution in the numerical calculation although the Reynolds number is low because of the computation time and memory capacity problem. The discussions on the calculated results give the following results : (1) Since the planform of the hydrofoil is elliptic, the ratio of cavity length to chord length becomes almost constant along the span when the cavity is small. But as the cavity grows, the tip region begins to generate larger cavity. The reason for this is that the tip vortex expands the separating flow region on the suction side of the hydrofoil near the tip.(2) The larger cavity weakens the tip vortex because of the reduction of the lift force and/or the diffusion of flow due to cavity. The diffusion due to cavity also increases the width of its wake.(3) The above calculated results agrees qualitatively with the existing experimental results. It can be said that even the present calculation with low Reynolds number has clarified many of the mechanisms of cavitating flow around a finite span hydrofoil.

Tip Vortex Cavitation Inhibition by Drag-Reducing Polymer Solutions

This paper presents previous and recent results obtained by the authors concerning the modification of the tip vortex cavitation of a finite span hydrofoil by drag-reducing polymer solutions. Experiments were conducted with homogeneous solutions and with semidilute solutions ejected at the tip of the wing. Measurements of the onset cavitation number for tip vortex cavitation, hydrodynamic forces on the hydrofoil and tangential velocities in the tip vortex have been conducted. The results show that tip vortex cavitation is inhibited in all cases but for different reasons. In homogeneous polymer solutions the lift of the hydrofoil, and hence the circulation, is considerably reduced leading to a less intense vortex as shown by tangential velocity measurements. With semidilute polymer solution ejections there is no noticeable change of the hydrodynamic forces but a significant modification of the tangential velocities in the core region. The mechanism for tip vortex cavitation inhibition is thus completely different in these two situations.

Unsteady theory of the hydrofoil of finite span

A three-dimensional unsteady flow around the hydrofoil has been dealt with in this paper. Under the assumption of infinitesimal wave and thin hydrofoil, analytic solution of perturbation velocity potential induced by the unsteady flow of a hydrofoil which is simplified as a series of rectangular vortex rings is achieved and then the unsteady forces can be evaluated.

A Partially Cavitating Hydrofoil of Finite Span

A Partially Cavitating Hydrofoil of Finite Span

Lifting‐line Theory of Supercavitating Hydrofoil of Finite Span

AbstractLifting‐line theory is developed for a supercavitating hydrofoil of finite span at non‐zero cavitation number. Main treatments in the paper are enumerated as follous: Simplification of basic equations in the perturbed flow field for a supercavitating hydrofoil of large aspect ratio shows that two‐dimensionality still holds with respect to an effective angle of attack over the span. Making use of this result, an integral equation is derived for the circulation distribution over the span at non‐zero cavitation number and then its numerical method of solution is shown. Foil characteristics are obtained analytically from circulation calculated and also discussed in details in relation to the aspect ratio and cavitation number. Particularly, a three dimensional correction factor is introduced to the supercavitating hydrofoils of finite span. Comparisons with the experimental data and former theories are made to confirm the appropriateness of the present theory.

Lifting-Line Theory of Supercavitated Hydrofoil of Finite Span

Lifting-Line Theory of Supercavitated Hydrofoil of Finite Span

Deformation of the water surface behind a hydrofoil of finite span

On the basis of the results of [1], a study is made of the variation of the water level behind a horizontal hydrofoil, and an approximate method is proposed for computing the fall (or rise) of the water level at high speeds.

The Wave and Induced Drag of a Hydrofoil of Finite Span in Water of Limited Depth

The wave resistance and the induced drag of a simple hydrofoil of finite span moving at a fixed submergence in water of finite depth are derived from a knowledge of the shallow water potential of a source. From this the waves produced by the semi-infinite doublet sheet which represents the undisturbed mathematical model of the hydrofoil are computed and the wave resistance is then inferred from the formula for the waves. Special cases which have been published previously are recaptured from the formulas. The induced drag is computed from a knowledge of the nature of the potential functions needed to satisfy the boundary conditions on the bottom and free surface. A comparison with one set of experimental data shows the theory to underestimate the experimentally determined lift-dependent drag curve at low Froude numbers F and to agree very well as high F. It is conjectured that the lack of good agreement at low F is due to the neglect of the influence of the free surface on the lift which has been omitted in this analysis.

Evaluation of the Theory for the Flow Pattern of a Hydrofoil of Finite Span

Expressions for various properties of the flow field aft of a finite-span hydrofoil in smooth water are presented and discussed in this paper. Potential functions for the motion that have been derived previously on the basis of linearized free-surface theory serve as the basic terms from which the flow field is derived. Both two-dimensional and three-dimensional theories are used, and the expressions derived for the surface-wave elevation and downwash from the various theories are compared with experimental values. As a result of this study, it is shown that three-dimensional effects are of great importance and hence terms derived from the two-dimensional theory do not accurately represent the true flow properties. Recommended formulas, whose validity is demonstrated by the comparison with the limited data presented herein, are given for the evaluation of both the surface-wave amplitude and downwash.

Wall Effect on the Characteristics of the Submerged Hydrofoil of Finite Span

From the standpoint of lifting-line theory, the wall effect of tank side is considered on the lift and resistance of the submerged hydrofoil of finite span.The main results obtained are as follows(1) The lift increases and the resistance decreases due to the wall effect, but those amounts are comparatively small.(2) A correcting method for the wall effect is proposed.(3) A minimum allowable breadth of the experimental tank for neglecting the wall effect should be more than twice span of the submerged hydrofoil.(4) Some special cases are examined and compared with the previous results.

Application of Ship-Wave Theory to the Hydrofoil of Finite Span

It is demonstrated in this paper2 that the deepwater wave drag of a hydrofoil of finite span can be found directly from the theory developed largely for ship hydrodynamics by Havelock and others. The wave drag is then studied at high Froude numbers and from the observed behavior the induced drag of the hydrofoil can be deduced from existing aerodynamic formulas. Evaluation of the resulting formulas is effected for two arbitrary load distributions and a comparison with some model test results is made. A practical approximation which gives the influence of gravity over a range of high Froude numbers is found and from this one can deduce a Froude number beyond which the effects of gravity may be ignored. It is also shown that an expression for the waves at some distance aft of the hydrofoil can be deduced from the general formulas developed for ship hydrodynamics. A discussion of the wave pattern is given with particular emphasis on the centerline profile at high Froude numbers and a contrast is pointed out in regard to the results of the two-dimensional theory for the hydrofoil waves and wave resistance.

A Calculating Method for Characteristics of the Submerged Hydrofoil of Finite Span (The 2nd Report)

The main problems treated in this paper are as follows (1) Comparison of the measured value in NACA tank with the calculated by the author's, method.(2) A calculating method for characteristics of the submerged hydrofoil of a dihedral angle. In §2, the calculated lift and resistance are compared with the measured in NACA tank, from which it can be safely said that the accuracy of the calculating method proposed is reasonably good for the ordinary aspect ratio of the submerged hydrofoil In §3, a calculating method for characteristics of the submerged hydrofoil of a dihedral angle is proposed from the standpoint of the liftingline theory and wave resistance theory. Numerical calculations are made and it is shown that the numerical results are in good accordance with the American's empirical formula and Tinney's results.In §4, the characteristics of the submerged hydrofoil of vertical finite span are examined in connection with the ship rudder which can be obtained as a special case.In §5, the surface waves caused by the submerged hydrofoil of a dihedral angle are examined.